git.distorted.org.uk Git - u/mdw/catacomb/blob - calc/ecp.cal

   1 /* -*-apcalc-*-
   2  *
   3  * $Id: ecp.cal,v 1.5 2004/04/08 01:36:15 mdw Exp $
   4  *
   5  * Testbed for elliptic curve arithmetic over prime fields
   6  *
   7  * (c) 2000 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Object types ------------------------------------------------------*/
  31
  32 obj ecp_curve { a, b, p };
  33 obj ecp_pt { x, y, e };
  34
  35 /*----- Main code ---------------------------------------------------------*/
  36
  37 define ecp_curve(a, b, p)
  38 {
  39   local obj ecp_curve e;
  40   e.a = a;
  41   e.b = b;
  42   e.p = p;
  43   return (e);
  44 }
  45
  46 define ecp_pt(x, y, e)
  47 {
  48   local obj ecp_pt p;
  49   p.x = x % e.p;
  50   p.y = y % e.p;
  51   p.e = e;
  52   return (p);
  53 }
  54
  55 define ecp_pt_print(a)
  56 {
  57   print "(" : a.x : ", " : a.y : ")" :;
  58 }
  59
  60 define ecp_pt_add(a, b)
  61 {
  62   local e, alpha;
  63   local obj ecp_pt d;
  64
  65   if (a == 0)
  66     d = b;
  67   else if (b == 0)
  68     d = a;
  69   else if (!istype(a, b))
  70     quit "bad type arguments to ecp_pt_add";
  71   else if (a.e != b.e)
  72     quit "points from different curves in ecp_pt_add";
  73   else {
  74     e = a.e;
  75     if (a.x == b.x) {
  76       if (a.y != b.y) {
  77         return (0);
  78       }
  79       alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p;
  80     } else
  81       alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p;
  82
  83     d.x = (alpha^2 - a.x - b.x) % e.p;
  84     d.y = (-a.y + alpha * (a.x - d.x)) % e.p;
  85     d.e = e;
  86   }
  87
  88   return (d);
  89 }
  90
  91 define ecp_pt_dbl(a)
  92 {
  93   local e, alpha;
  94   local obj ecp_pt d;
  95   if (istype(a, 1))
  96     return (0);
  97   e = a.e;
  98   alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p;
  99   d.x = (alpha^2 - 2 * a.x) % e.p;
 100   d.y = (-a.y + alpha * (a.x - d.x)) % e.p;
 101   d.e = e;
 102   return (d);
 103 }
 104
 105 define ecp_pt_neg(a)
 106 {
 107   local obj ecp_pt d;
 108   d.x = a.x;
 109   d.y = a.e.p - a.y;
 110   d.e = a.e;
 111   return (d);
 112 }
 113
 114 define ecp_pt_check(a)
 115 {
 116   local e;
 117
 118   e = a.e;
 119   if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p)
 120     quit "bad curve point";
 121 }
 122
 123 define ecp_pt_mul(a, b)
 124 {
 125   local p, n;
 126   local d;
 127
 128   if (istype(a, 1)) {
 129     n = a;
 130     p = b;
 131   } else if (istype(b, 1)) {
 132     n = b;
 133     p = a;
 134   } else
 135     return (newerror("bad arguments to ecp_pt_mul"));
 136
 137   d = 0;
 138   while (n) {
 139     if (n & 1)
 140       d += p;
 141     n >>= 1;
 142     p = ecp_pt_dbl(p);
 143   }
 144   return (d);
 145 }
 146
 147 /*----- FIPS186-2 standard curves -----------------------------------------*/
 148
 149 p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1,
 150                  6277101735386680763835789423207666416083908700390324961279);
 151 p192_r = 6277101735386680763835789423176059013767194773182842284081;
 152 p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012,
 153                 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192);
 154
 155 /*----- That's all, folks -------------------------------------------------*/
 156